Question

How do you sketch the graph of `y=(2x)^2` and describe the transformation?

Answer 1

See explanation

Explanation:

The equation gives you the following information:
Step Pattern: 4, 12, 20...
Vertex: (0,0)
X-Intercept(s): (0,0)
Y-Intercept: (0,0)

Therefore the graph should look like the following:
graph{y=(2x)^2 [-10, 10, -5, 5]}

To describe the transformation of the graph, follow RST (Reflection, Stretch/Compression, Translation). The description would be the following:
The parabola is stretched by a factor of 4.

Note: The parabola is not reflected and translated, therefore it is not described in the description.

Answer 2

By assigning value for x, find y.

Explanation:

If x is -2, you will get `y=16`
If x is -1, you will get `y=4`
If x is zero, y will be zero.
If x is +1, you will get `y=4`
If x is +2, you will get `y=16`
etc.

The graph is below.

graph{(2x)^2 [-9.33, 10.67, -0.92, 9.08]}